International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/4007 2020 2020 College of Business Administration in Hawtat Bani Tamim, Prince Sattam Bin Abdulaziz University, Al-Kharj, 11942, Saudi Arabia Anas Anas Uncertainty, imprecision, and incomplete information are commonly found in complex economic and financial systems, and traditional probabilistic models are thus inadequate to accurately model and forecast these systems. In this work, a new extension of the Muth distribution in the neutrosophic environment is presented leading to the neutrosophic Muth distribution (NMD). This new model introduces neutrosophic parameters aiming to quantify vague and uncertain information and provides a flexible and robust approach to modeling right-skewed economic data. Some key characteristics including the density function and cumulative distribution function, moment generating function, and origin moments are obtained in the neutrosophic framework. The study of a model treated under uncertainty is described and an inferential method transforming it into neutrosophic maximum likelihood by interval-valued data is discussed. A real-world financial dataset is considered in order to prove the usefulness of the proposed distribution. The findings emphasize that the proposed distribution has the potential to be a comprehensive, flexible, and potential model for handling uncertainty in economics and finance data. 2026 2026 95 109 10.54216/IJNS.270209 https://www.americaspg.com/articleinfo/21/show/4007